Notes

Correlation: a strong relationship does not necessarily mean a high correlation if the relationship is non-linear (Wainer).

A correlation is profoundly affected by an outlier; always look at the plot (Wainer).

The assumptions made for ANOVA (and many other statistical analysis), therefore, are additivity of components of variation, independence of the observations, homogeneity of variances, and normality of the observations. These assumptions unfortunately are too often ignored in day-to-day analysis of scientific data.

If our data violate the assumptions, there are two alternatives. The first option may be to apply a different suite of statistical tests that make no assumptions about distributions. Below we discuss nonparametric equivalents of parametric methods that can be applied to data that do not meet the assumptions of parametric tests. The second option is to transform the data into new scales that do meet the assumptions, and then carry out the appropriate ANOVA on the transformed data.